I believe the difference between illegal and unlawful was the difference between black and white listing. As in, illegal means a specific act is banned and unlawful means doing something outside of what was prescribed for that situation.
I don't think there's a large moral component to the respective use of each word, it's more of a mathematical concept. That said, odds are "DON'T DO THAT" is usually going to have a stronger moral force behind it than "YOU CAN ONLY DO IT THIS WAY" since people can come up with creative situations that weren't thought of at the time the law was written, and of course it varies based on the situation (people will probably be more pissy if you handle nuclear material in an unlawful way than if you jaywalk for instance).
Worth remembering it's tort not crime.
[Not that you're saying it's criminal, just that sometimes illegal is taken to mean criminal whilst torts and such are described instead as unlawful.]